Let's say you have have a file containing a car body, and another file containing wheels and tires for that car. If you append the tires to the car, you copy the meshes of the tires into the file for the car. If you link the file containing the tires to the file containing the car, you do not copy the meshes into the file for the car, but as long as both files are available, the tires will seem to appear when the file is viewed or rendered.

Linking the tires will result in a smaller file, as one can use multiple links to the same file to show the tires, but at the expense that if the file containing the tires becomes unavailable, then the tires will not be displayed. Appending the tires makes the tires always available when the car is available, because they have been incorporated into the file with the car, but at the cost of a larger file size.